Robert, I feel your pain!
I had a similar Geico experience with my son's Camaro. They will give you a complete printout with the results of their research on the 968's value. You can supply support information that may raise the value and change the outcome, but from my experience they are polite but inflexible. You also have the option of canceling the claim and fixing the car out of your pocket. Another option is to part out your baby and get another 968...I cringe, even as I type these words.
Flash was able to find 2 beauties in a very short time, so maybe this is not an impossible task. This will also remove the "loss" from your policy and will save you insurance money with them or another carrier.
I hope that you save your baby!
Good Luck!
Brian